Questions: Find the exact value of sin O in simplest radical form.

Transcript text: Find the exact value of $\sin O$ in simplest radical form.

Solution

Step 1: Identify the relevant sides of the triangle.

In right triangle OPQ, the side opposite angle O is PQ, and the hypotenuse is OQ. We are given PQ = 3 and OQ = √61.

Step 2: Calculate sin O.

The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore,

sin O = PQ/OQ = 3/√61.

Step 3: Rationalize the denominator.

To simplify the expression, we rationalize the denominator by multiplying the numerator and denominator by √61:

sin O = (3/√61) * (√61/√61) = (3√61)/61.

\$\boxed{\sin O = \frac{3\sqrt{61}}{61}}\$

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